A teen wonders how to directly plot an absolute value that appears to have more than two distinct
intervals. Thanks to the function's continuity, Doctor Peterson picks up where she left
off to re-write the pieces into something easier to visualize.

A student struggles to identify a pair of positive integers, given their sum as well as the
sum of their greatest common factor and least common multiple. Doctor Greenie
applies some algebra and factorization to turn the problem into a Diophantine
equation.

A young adult seeks positive integer solutions to 2a^2 = b^2 +
c^2. Doctor Carter obliges by setting up a comparable problem in
the Cartesian plane — for points on a circle of radius two
— and seeking its rational solutions.

As I read various algebra books for high school kids, I find what
appears to be an inconsistent use of the words 'quadratic equation',
and I wanted to be sure I use it correctly myself. Is it correct to
call y = ax^2 + bx + c a 'quadratic equation', or a 'quadratic function'?